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J & K CET Engineering J and K - CET Engineering Solved Paper-2012

  • question_answer
    If \[^{m+n}P{{  }_{2}}=90\] and \[^{m-n}P{{  }_{2}}=30,\] then \[(m,n)\] is given by (where, m and n are positive integers)

    A)  \[(8,\,2)\]          

    B)  \[(5,\,\,6)\]

    C)  \[(3,\,\,7)\]           

    D)  \[(8,\,\,3)\]

    Correct Answer: A

    Solution :

    By taking option [a], \[(m,\,n)=(8,\,2)\] Now, \[^{m+n}{{P}_{2}}{{=}^{8+2}}{{P}_{2}}{{=}^{10}}{{P}_{2}}\] \[=\frac{10\,!}{8!}=90\] and \[^{m-n}{{P}_{2}}{{=}^{8-2}}{{P}_{2}}{{=}^{6}}{{P}_{2}}\] \[=\frac{6!}{4!}=30\]


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